A theory that describes how matter produces and responds to the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.
1
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2answers
78 views
Coordinate and conformal transformations of the FRW metric
I'm considering a metric of the following form (signature $(+,-,-,-)$):
$$ds^2 = (F(r,t)-G(r,t))dt^2 - (F(r,t)+G(r,t))dr^2 - r^2(d\Omega)^2$$
where $F(r,t)$ and $G(r,t)$ are arbitrary scalar ...
1
vote
0answers
37 views
Ex 0.2.1 in Sachs and Wu's textbook
In the next attachements are:
1. Exercise 0.2.5 which I want help with.
Proposition 0.2.1 and its proof.
Now, basically a few things are changed in the theorem, I don't think I can use here the ...
3
votes
2answers
157 views
Understanding Einstein's field equation
Einstein's field equation:
$$G_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu} - g_{\mu\nu}\Lambda$$
I'm trying to understand each of the terms in this equation intuitively, but I'm struggling.
Basically, ...
7
votes
3answers
547 views
Why is a black hole black?
In general relativity (ignoring Hawking radiation), why is a black hole black? Why nothing, not even light, can escape from inside a black hole? To make the question simpler, say, why is a ...
7
votes
1answer
149 views
Why is Einstein gravity not renormalizable at two loops or more?
(I found this related Phys.SE post: Why is GR renormalizable to one loop?)
I want to know explicitly how it comes that Einstein-Hilbert action in 3+1 dimensions is not renormalizable at two loops or ...
6
votes
2answers
439 views
Does perturbation theory break down for quantum gravity?
Perturbation theory presumes we have a valid family of models over some continuous (infinitely differentiable, in fact) range for some parameters, i.e. coupling constants. We have some special values ...
3
votes
2answers
352 views
Lorentz invariance of the 3 + 1 decomposition of spacetime
Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example
$$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$
($N$ is called lapse, $N_a$ is ...
1
vote
3answers
147 views
What truly is mass, and is there a direct way to measure it?
We know a mass of an object of one kilogram as an object that weighs W = mg = 9.8 N and we reference it to that, (when it should as a fundamental parameter describe weight not the opposite). But if we ...
6
votes
2answers
174 views
What is the definition of a timelike and spacelike singularity?
What is the definition of a timelike and spacelike singularity?
Trying to find, but haven't yet, what the definitions are.
0
votes
2answers
110 views
Einstein's theory tells us that gravity is a curve in space and time but how does that causes attraction in mass? [duplicate]
The sun is incredibly massive object and it causes the space around it to bend. This causes the planets to pulled to the sun or the planets move in an elliptical path around the sun. But I don't ...
2
votes
4answers
204 views
Time inside a Black hole
If time stops inside a black hole, due to gravitational time dilation, how can it's life end after a very long time? If time doesn't pass inside a black hole, then an event to occur inside a black ...
1
vote
1answer
119 views
Deriving the conservation of mass in a perfect fluid
I have a problem on a homework assignment. I will write the question and then what I have so far. I just want some guidance on what I am doing wrong (or right). Any help would be greatly appreciated:
...
1
vote
1answer
71 views
Can the fuzzball conjecture be applied to microscopically explain the entropy of a region beyond the gravitational observer horizon?
In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime.
If I ...
0
votes
1answer
83 views
Space time curvature real or theoretical (mathematical)?
Assuming one were in a capsule of some kind, with no window or instruments, and you swung into the gravitational field of a massive object (planet). Assuming no atmosphere to provide friction, could ...
6
votes
1answer
103 views
Why is $R^2$ gravity not unitary?
I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity?
My naive ...
2
votes
1answer
109 views
Privileged coordinate system (or lack thereof) in general relativity
What does the following statement mean and why is it true?
The Weak Equivalence Principle (WEP) implies that in general curved space-time there is no privileged coordinate system.
I have looked ...
0
votes
0answers
33 views
What is the physical meaning of charges at light-like infinity in asymptotically flat space-times?
In the case of charges defined at space-like infinity, I can understand the physical meaning of them because they can be related to measurements made by a physical observer (that is an observer whose ...
3
votes
1answer
155 views
Calculating Riemann Tensor Using Tetrad Formalism
I was trying to calculate the Riemann Tensor for a spherically symmetric metric:
$ds^2=e^{2a(r)}dt^2-[e^{2b(r)}dr^2+r^2d\Omega^2]$
I chose the to use the tetrad basis:
$u^t=e^{a(r)}dt;\, ...
1
vote
3answers
137 views
About gravity through space time curvature
Is it possible to produce virtual gravity? I mean gravity without the help of mass by curving spacetime with other effects like fast rotating objects?
4
votes
2answers
191 views
What is the variation of Gauss-Bonnet term a total derivative of?
What is the variation of Gauss-Bonnet term total derivative of?
i.e. Variation of Gauss-Bonnet combination $= \nabla_{\mu} C^{\mu}$.
What's $C^{\mu}$ in 4-dimensions?
2
votes
2answers
108 views
Different approaches to calculating the Christoffel symbols
I would be very grateful to whoever can debug the following calculations...
We have the metric for static spacetime: $$ds^2 = -\exp(2U(\vec x))dt^2+h_{ij}(\vec x) d x^i d x^j$$
I want to find the ...
4
votes
3answers
139 views
How do you tell if a metric is curved?
I was reading up on the Kerr metric (from Sean Carroll's book) and something that he said confused me.
To start with, the Kerr metric is pretty messy, but importantly, it contains two constants - ...
4
votes
1answer
190 views
Boundary conditions of relativistic wave solutions?
If you take Einstein's field equations,
\begin{equation}
R_{\mu\nu}-\tfrac{1}{2}g_{\mu\nu}R = -\kappa T_{\mu\nu},
\end{equation}
and you insert the metric
\begin{equation}
g_{\mu\nu} = \eta_{\mu\nu} ...
3
votes
2answers
78 views
Runge-Lenz vector and Keplerian Orbits
Is the loss of closed Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?
0
votes
0answers
41 views
Switching from an accelerated frame of reference to a locally inertial reference system
Using the equivalence principle, show that the interval for an accelerated observer ($\textbf{g}$ uniform and constant) has the form
$$
ds^2|_{\text{first order in ...
3
votes
2answers
110 views
Difference between slanted indices on a tensor
In my class, there is no distinction made between,
$$
C_{ab}{}^{b}
$$
and
$$
C^{b}{}_{ab}.
$$
All I know, and read about so far, is the distinction of covariant and contravariant, form/vector, etc. ...
1
vote
0answers
44 views
Dust generated static space-time implications on fluid 4-velocity
Imagine we have a perfect fluid with zero pressure (dust), which generates a solution to Einstein's equations. Show that the metric can be static only if the fluid four-velocity is parallel to the ...
0
votes
1answer
52 views
Help me to understand this conversion (4-vectors)
$u^{\mu}$ - 4-velocity
$b^{\mu}$ - 4-vector of magnetic field
$
u_{\mu}u^{\mu}=-1, \qquad u_{\mu}b^{\mu}=0
$
$$
...
0
votes
0answers
93 views
covarient derivative of electromagnetic field tensor
I'm trying to prove the energy momentum tensor in curved spacetime for Electromagnetic field is Divergence-less directly(Without using general lie derivative method which can prove any energy momentum ...
2
votes
0answers
31 views
Are there functions of the metric that are scalars under spatial diffs up to total derivatives?
Let $g_{\mu\nu}$ be a metric on a manifold with a time direction $x^0$ singled out. I'm wondering if there exists a function $F(g_{\mu\nu},\partial_\rho g_{\mu\nu},\ldots)$ that transforms under ...
5
votes
0answers
78 views
Do semiclassical GR and charge quantisation imply magnetic monopoles?
Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how?
(I am not ...
2
votes
4answers
125 views
Does everything with mass or energy have a gravitational pull?
As small as it may be, does every 'thing' have a gravitational pull? That is, something with mass or energy. No matter how obsolete or negligible it may be, is it there? If so, how is it calculated? ...
4
votes
2answers
282 views
Action for a point particle in a curved spacetime
Is this action for a point particle in a curved spacetime correct?
$$\mathcal S =-Mc \int ds = -Mc \int_{\xi_0}^{\xi_1}\sqrt{g_{\mu\nu}(x)\frac{dx^\mu(\xi)}{d\xi} \frac{dx^\nu(\xi)}{d\xi}} \ \ d\xi$$
12
votes
3answers
703 views
No hair theorem for black holes and the baryon number
The no hair theorem says that a black hole can be characterized by a small number of parameters that are visible from distance - mass, angular momentum and electric charge.
For me it is puzzling why ...
4
votes
2answers
348 views
Does spacetime in general relativity contain holes?
Are there physical models of spacetimes, which have bounded (four dimensional) holes in them?
And do the Einstein equations give restrictions to such phenomena?
Here by holes I mean ...
2
votes
5answers
251 views
Einstein gravity versus Newton's gravity
What's the basic difference between the gravity as seen by Einstein, and that by Newton?
5
votes
2answers
309 views
What is the likelihood of ever discovering the graviton?
How would one look for and confirm existence of a graviton?
Someone was speaking to me about perhaps one day discovering the graviton, but to me it seems unlikely, although I'm young and essentially ...
1
vote
0answers
104 views
Use of Principle of Equivalence
Let $x^\mu$ be the coordinates of a reference frame, $K$, where all bodies feel the same constant and uniform acceleration $\textbf{a}=\textbf{g}=-\nabla\varphi$; let $\xi^\mu$ be the coordinates of a ...
-3
votes
4answers
190 views
How can we be sure about the constancy of atomic clocks as in the Hafele and Keating time dilation test?
Atomic clocks were used in Hafele and Keatings experiment which supposedly helped to prove time dilation.
Time Dilation Proof - Hafele and Keating
How can we be sure other forces didn't act upon the ...
0
votes
2answers
134 views
Advanced Heaviside-Feynman formula implies electromagnetic inertia?
The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point $P$ due to an arbitrarily moving charge $q$
$$ ...
1
vote
2answers
137 views
How to find a curvature of the space-time by having $g^{\alpha \beta}$ in the following case without cumbersome calculations?
The metric tensor for Fock-Lorentz space-time,
$$
\mathbf r_{||}{'} = \frac{\gamma (u)(\mathbf r_{||} - \mathbf u t)}{\lambda \gamma (u) (\mathbf u \cdot \mathbf r) + \lambda c^{2} (1 - \gamma (u))t + ...
3
votes
2answers
91 views
Gravitational distortion of an object's diameter, at a distance,
Does the curvature of space-time cause objects to look smaller than they really are? What is the relationship between the optical distortion and the mass of the objects?
17
votes
3answers
807 views
Does gravity slow the speed that light travels?
Does gravity slow the speed that light travels? Can we actual measure the time it takes light from the sun to reach us? Is that light delayed as it climbs out of the sun's gravity well?
2
votes
1answer
68 views
Difference between proper and comoving frames
I'm reading this book "Introduction to Quantum Fields in Classical Backgrounds" by Mukhanov & Winitzki, and there in the chapter 8 "The Unruh Effect" they introduce 3 reference frames.
Laboratory ...
10
votes
1answer
120 views
Have general relativistic effects of the sun's rotation been measured?
I was wondering if general relativistic effects of the sun's rotation have also been measured, like gravity probes A and B measured GR effects from the earth.
2
votes
1answer
176 views
Cosmological constant
I have always wondered about how cosmological constant is characterized. So since it is still a hypothesis you often read the “cosmological constant measured to be ….”. Shouldn't the statement read ...
1
vote
1answer
58 views
Pound-Rebka-Snider experiment in the inertial frame
In Schutz's book (page 120), Schutz first derives the gravitational redshift in the PRS experiment in a previous paragraph.
$\frac{\nu^{\prime}}{\nu}=\frac{m}{m+mgh+O(v^4)}=1-gh+O(v^4)$.
Here ...
0
votes
1answer
34 views
Is weak lensing the statistical effect of microlensing?
I am looking into the effects of gravitational lensing of gravitational waves. I know that gravitons travel along null geodesics, just as photons, and so they will suffer the same deflection angle by ...
2
votes
3answers
110 views
What does it mean that a wavevector is null?
I have derived geometric optics for gravitational waves and I am trying to interpret one of the results. I have
\begin{equation}
k_{\rho}k^{\rho}=0
\end{equation}
for the wavevector. For the case ...
3
votes
1answer
133 views
Change of coordinates from an arbitrary frame to a locally inertial frame in General Relativity
If I have the following metric:
$$ds^2=(1-2\phi)c^2 dt^2 - (1-2 \phi)(dx^2+dy^2+dz^2)$$
$\phi$ being the gravitational potential with $|\phi| << 1$ everywhere.
How do I find a coordinate ...
